Author: Dann Corbit
Date: 12:17:00 01/12/01
Go up one level in this thread
On January 12, 2001 at 15:09:28, Robin Smith wrote: >On January 11, 2001 at 21:41:45, Dann Corbit wrote: > >>When we are talking about qualities I agree with you. When we are talking about >>PROOFS mathematics is THE ONLY WAY to accomplish that. > >Dan, > >I agree with many of the arguments you have been making in this thread, but in >some cases it seems you go way over board. For example, the above is a rather >extreme statement, don't you think? In a US criminal court of law, there is the >concept of "proof beyond a reasonable doubt", and yet I doubt there are very >many arguments that lawyers make which would be classified as mathematical >proofs. I agree that a mathematical proof is the most formal and rigorous kind >of proof, but it is certainly not "THE ONLY WAY" to prove something. Clearly >the definition of "proof" that the lawyers had in mind is not the same >definition of "proof" that you are using. Different people have different ideas >of what constitutes proof. Yours is a mathematical definition, but that does >not mean other definitions are invalid, just different. Mathematical proofs may >be the least prone to error, but that does not make them the "only way", nor >does it make them infallible. Even mathematical proofs are sometimes wrong. The proof of a court is similar to what I am seeking. Proof beyond a reasonable doubt. Right now, there is a reasonable doubt. >Also, if you want 100% mathematical certainty, a mathematical/statistically >based argument can NEVER "prove" that someone is of "GM strength", even if they >win 100% of the games they play against GM's and they play hundreds of games. We will never achieve 100% certainty, because it is impossible. But we have far less than 50% certainty. Does that sound like something that is proven to you? Less than a coin toss? >The uncertainty in the claim that they are GM strength becomes very, very small >.... but it never goes to zero. Mathematically there will always be a small, >but non-zero, chance that they were very, very "lucky". Agreed. I'm not as unreasonable as you might imagine. (Well, most of the time I am not). I am not looking for 100% certainty. I am looking for reasonable certainty. I also reject the helter-skelter conditions of the experiments. Without adequate controls and repeatability, experiments are worthless. >Right now we can already say, statistically, Rebel IS GM strength. It is just >the uncertainty in the validity of that statement that is still quite large. As >more games are played and the uncertainty goes down, we will have more >confidence that the assertion is true (or not, as subsequent data suggests). >There is no magic number of games at which point we have suddenly "proved >mathematically" that computers are (or are not) GM strength. Right now, the uncertainty is so large that it is clearly not proven. It is probably true. It simply has not been proven to be so. I don't think it is even proven beyond a reasonable doubt. In fact, I don't think it is even proven to the level of a civil case (where the preponderance of the evidence says it is so). But that one is iffy, I will admit. I have pointed out many flaws in the model, and suggested reasonable assertions that demonstrate how the experients are flawed and how the ratings could change dramatically. All that having been said, they are very likely GM's. But it will be proven when it has been proven. Right now it isn't.
This page took 0 seconds to execute
Last modified: Thu, 15 Apr 21 08:11:13 -0700
Current Computer Chess Club Forums at Talkchess. This site by Sean Mintz.